### Research

My research area is in algebraic number theory with connections to arithmetic geometry, algebraic topology, and group theory. I am specifically interested in Galois actions.
### Publications and preprints

R. Davis, R. Pries, K. Wickelgren ** The Galois action on the lower central series of the fundamental group of the Fermat curve**, submitted August 2018.

R. Davis and R. Pries ** Cohomology groups of Fermat curves via ray class fields of cyclotomic fields**, submitted July 2018.

R. Davis and E. H. Goins ** Arithmetic of quaternion origami**, May 2018.

R. Davis ** A note on the procedure to find the generic polynomial of a quotient (closely following Adelmann)**, May 2018.

R. Davis, R. Pries, V. Stojanoska, and K. Wickelgren ** The Galois action and cohomology of a relative homology group of Fermat curves**, J. Algebra, 505: 33-69, 2018. See the Magma files of computuations for the paper.

A.C. Cojocaru, R. Davis, A. Silverberg, and K.E. Stange, ** Arithmetic properties of the Frobenius traces defined by a rational abelian variety,** with two appendices by J-P. Serre. International Mathematics Research Notices, vol. 2016, pages 1-46.

R. Davis, R. Pries, V. Stojanoska, and K. Wickelgren **Galois action on the homology of Fermat curves**, Directions in Number Theory: proceedings of the 2014 WIN3 workshop, Springer XV, pages 57-86.

R. Davis ** Images of metabelian Galois representations associated to elliptic curves** Women in numbers 2: research directions in number theory, 29-46, Contemp. Math., 606, Centre Rech. Math. Proc., Amer. Math. Soc., Providence, RI, 2013.

R. Davis (advisor N. Boston) Thesis (2013).

A. Brouwer, R. Davis, A. Larkin, D. Studenmund, and C. Tucker ** Intrinsically S^1 3-linked graphs and other aspects of S^1 embeddings** Rose-Hulman Institute of Technology Undergraduate Math Journal (2007).